LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
f|I|0.70711 MHzf1​f2​BW = 50 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 50 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 50 kHz
Q =
2.Easy
f|I|0.707110 kHzf1​f2​BW = 1.25 kHz

A resonance curve peaks at 10 kHz, and its half-power points are 1.25 kHz apart. Find the quality factor Q.

f0 = 10 kHzBW = 1.25 kHz
Q =
3.Medium
V1 kΩ4.7 mH470 nF

A parallel RLC circuit has R = 1 kΩ, L = 4.7 mH and C = 470 nF. Find its quality factor Q.

R = 1 kΩL = 4.7 mHC = 470 nF
Q =
4.Medium
V100 Ω10 mH2.2 nF

A series RLC circuit has R = 100 Ω, L = 10 mH and C = 2.2 nF. Find its bandwidth BW in kHz.

R = 100 ΩL = 10 mHC = 2.2 nF
BW = kHz
5.Hard
C = 10 nFR = 20 ΩL = 100 mH

A charged 10 nF capacitor discharges through a 100 mH coil with a total series resistance of 20 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 100 mHC = 10 nFR = 20 Ω
n =
6.Hard
VR = ?2.2 mHC

A series resonant circuit uses a 2.2 mH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 2.2 mHBW = 100 kHz
R = Ω

Answer key

  1. 1. Q = 20
  2. 2. Q = 8
  3. 3. Q = 10
  4. 4. BW = 1.592 kHz
  5. 5. n = 34.89
  6. 6. R = 1382 Ω

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